On the determination of magnetic grain‐size distributions of superparamagnetic particle ensembles using the frequency dependence of susceptibility at different temperatures

SUMMARY Magnetic grain‐size and coercivity distributions of a superparamagnetic (SP) particle ensemble together determine its frequency dependence of susceptibility (FDS). Investigating the mathematical theory of this dependence leads to a general dispersion relation between real and imaginary parts of the complex susceptibility for SP particle ensembles, which extends the previous treatment by Néel. Using the new theory, it is demonstrated that the inverse problem of determining the combined grain‐size and coercivity distribution from FDS measurements is not uniquely solvable. The inversion of the FDS at one temperature can be described by a deconvolution integral, the kernel of which is analytically calculated. The deconvolved FDS corresponds to an energy barrier distribution. Only using a priori assumptions about the relation between particle volume and coercivity it can be interpreted in terms of a volume or grain‐size distribution. In order to deconvolve natural rock measurements, a semi‐analytical parametric deconvolution method has been developed, which allows to reconstruct the SP grain‐size distribution even from relatively noisy data. Dense measurements of FDS at several temperatures can be used to check for the applicability of the above theory. Observed deviations can be interpreted in terms of magnetostatic particle interaction. A quantitative estimate is presented, which allows to determine the average interaction field together with the volume distribution.